TABLE OF CONTENTS This appendix reviews the basic results for many of the distributions which are useful in mobile communications and is associated mainly with Chapter 2. The distributions are motivated by the need for descriptions for the electrical and field signals and the signal coverage and communications outage, etc. Gaussian statistics form the basis of most of the distributions. No physical modelling is included here so that the statistics are confined to envelope and power, and some phase distributions. The distributions of phase derivatives, for example, from physical models, are treated in the text and make use of the results here. The overbar and the angle brackets are used interchangeably with the usual expectation operator for simplicity here. Similarly, whereas in classical statistical notation, upper case letters are normally used for a random variable, this is not adhered to in this text.
The Gaussian distribution is the most important probability density because it models more random processes than any other distribution. This is also evident from the central limit theorem which results in Gaussian statements for the sum or average of almost any random variables. The asymptotic sum of random variables is a Gaussian quantity. Thermal noise (sum of the effect of electrons in motion) is therefore Gaussian, an example which is particularly close to the heart of the communications engineer. In mobile and other multipath communications, the signals, both wanted and unwanted, are again summations of components. In linear signal combining, used to repair the multipath impaired channel, the...
